Showing papers on "Star formation published in 2000"

Control of Star Formation by Supersonic Turbulence

Abstract: Understanding the formation of stars in galaxies is central to much of modern astrophysics. However, a quantitative prediction of the star formation rate and the initial distribution of stellar masses remains elusive. For several decades it has been thought that the star formation process is primarily controlled by the interplay between gravity and magnetostatic support, modulated by neutral-ion drift (known as ambipolar diffusion in astrophysics). Recently, however, both observational and numerical work has begun to suggest that supersonic turbulent flows rather than static magnetic fields control star formation. To some extent, this represents a return to ideas popular before the importance of magnetic fields to the interstellar gas was fully appreciated. This review gives a historical overview of the successes and problems of both the classical dynamical theory and the standard theory of magnetostatic support, from both observational and theoretical perspectives. The outline of a new theory relying on control by driven supersonic turbulence is then presented. Numerical models demonstrate that, although supersonic turbulence can provide global support, it nevertheless produces density enhancements that allow local collapse. Inefficient, isolated star formation is a hallmark of turbulent support, while efficient, clustered star formation occurs in its absence. The consequences of this theory are then explored for both local star formation and galactic-scale star formation. It suggests that individual star-forming cores are likely not quasistatic objects, but dynamically collapsing. Accretion onto these objects varies depending on the properties of the surrounding turbulent flow; numerical models agree with observations showing decreasing rates. The initial mass distribution of stars may also be determined by the turbulent flow. Molecular clouds appear to be transient objects forming and dissolving in the larger-scale turbulent flow, or else quickly collapsing into regions of violent star formation. Global star formation in galaxies appears to be controlled by the same balance between gravity and turbulence as small-scale star formation, although modulated by cooling and differential rotation. The dominant driving mechanism in star-forming regions of galaxies appears to be supernovae, while elsewhere coupling of rotation to the gas through magnetic fields or gravity may be important.

The Stellar Population Histories of Early-Type Galaxies. II. Controlling Parameters of the Stellar Populations

Abstract: This paper analyzes single stellar population (SSP)–equivalent parameters for 50 local elliptical galaxies as a function of their structural parameters. The galaxy sample is drawn from the high-quality spectroscopic surveys of Gonzalez (1993) and Kuntschner (1998). The basic data are central values of SSP-equivalent ages, t, metallicities, [Z/H], and enhancement ratios, [E/Fe], derived in Paper I, together with global structural parameters including velocity dispersions, radii, surface brightnesses, masses, and luminosities. The galaxies fill a two-dimensional plane in the four-dimensional space of [Z/H], log t, log σ, and [E/Fe]. SSP age, t, and velocity dispersion, σ, can be taken as the two independent parameters that specify a galaxy's location in this hyperplane. The hyperplane can be decomposed into two subrelations: (1) a Z-plane, in which [Z/H] is a linear function of log σ and log t and (2) a relation between [E/Fe] and σ in which [E/Fe] is larger in high-σ galaxies. Velocity dispersion is the only structural parameter that is found to modulate the stellar populations; adding other structural variables such as Ie or re does not predict [Z/H] or [E/Fe] more accurately. Cluster and field ellipticals follow the same hyperplane, but their (σ,t) distributions within it differ. Most Fornax and Virgo cluster galaxies are old, with a only a small sprinkling of galaxies to younger ages. The field ellipticals span a larger range in SSP age, with a tendency for lower σ galaxies to be younger. The present sample thus suggests that the distribution of local ellipticals in the (σ,t) plane may depend on environment. Since the (σ,t) distribution affects all two-dimensional projections involving SSP parameters, many of the familiar scaling laws attributed to ellipticals may also depend on environment. Some evidence for this is seen in the current sample. For example, only Fornax ellipticals show the classic mass-metallicity relation, whereas other subsamples do not. The tight Mg-σ relations of these ellipticals can be understood as two-dimensional projections of the metallicity hyperplane showing it edge-on. At fixed σ, young age tends to be offset by high [Z/H], preserving Mg nearly constant. The tightness of the Mg-σ relations does not necessarily imply a narrow range of ages at fixed σ. Although SSP parameters are heavily weighted by young stars, modeling them still places tight constraints on the total star formation history of elliptical galaxies. The relation between [E/Fe] and σ is consistent with a higher effective yield of Type II SNe elements at higher σ. This might occur if the IMF is enhanced in massive stars at high σ, or if more SNe II–enriched gas is retained by deeper galactic potential wells. Either way, modulating Type II yields versus σ seems to fit the data better than modulating Type Ia yields. The Z-plane is harder to explain and may be a powerful clue to star formation in elliptical galaxies if it proves to be general. Present data favor a frosting model in which low apparent SSP ages are produced by adding a small frosting of younger stars to an older base population (assuming no change in σ). If the frosting abundances are close to or slightly greater than the base population, simple two-component models run along lines of constant σ in the Z-plane, as required. This favors star formation from well-mixed pre-enriched gas rather than unmixed low-metallicity gas from an accreted object.

The Origin of Star Formation Gradients in Rich Galaxy Clusters

Abstract: We examine the origin of clustercentric gradients in the star formation rates and colors of rich cluster galaxies within the context of a simple model where clusters are built through the ongoing accretion of field galaxies. The model assumes that after galaxies enter the cluster their star formation rates decline on a timescale of a few gigayears, the typical gas consumption timescale of disk galaxies in the field. Such behavior might be expected if tides and ram pressure strip off the gaseous envelopes that normally fuel star formation in spirals over a Hubble time. Combining these timescales with mass accretion histories derived from N-body simulations of cluster formation in a ΛCDM universe, we reproduce the systematic differences observed in the color distribution of cluster and field galaxies, as well as the strong suppression of star formation in cluster galaxies and its dependence on clustercentric radius. The simulations also indicate that a significant fraction of galaxies beyond the virial radius of the cluster may have been within the main body of the cluster in the past, a result that explains naturally why star formation in the outskirts of clusters (and as far out as 2 virial radii) is systematically suppressed relative to the field. The agreement with the data beyond the cluster virial radius is also improved if we assume that stripping happens within lower mass systems, before the galaxy is accreted into the main body of the cluster. We conclude that the star formation rates of cluster galaxies depend primarily on the time elapsed since their accretion onto massive virialized systems and that the cessation of star formation may have taken place gradually over a few gigayears.

The Stellar Population Histories of Local Early-Type Galaxies. I. Population Parameters

Abstract: This paper commences a series of investigations into the stellar populations of local elliptical galaxies as determined from their integrated spectra. The goal of the series is to determine the star formation and chemical evolution histories of present-day elliptical galaxies. The primary galaxy sample analyzed is that of Gonzalez, which consists of 39 elliptical galaxies drawn primarily from the local field and nearby groups, plus the bulge of Messier 31. Single-burst stellar population (SSP)–equivalent ages, metallicities, and abundance ratios are derived from Hβ, Mg b, and Fe line strengths using an extension of the Worthey models that incorporates nonsolar line-strength "response functions" by Tripicco & Bell. These functions account for changes in the Lick/IDS indices caused by nonsolar abundance ratios, allowing us to correct the Worthey models for the enhancements of Mg and other α-like elements relative to the Fe-peak elements. SSP-equivalent ages of the Gonzalez elliptical galaxies are found to vary widely, 1.5 Gyr t 18 Gyr, while metallicities [Z/H] and enhancement ratios [E/Fe] are strongly peaked around [Z/H] = +0.26 and [E/Fe] = +0.20 (in an aperture of radius re/8). The enhancement ratios [E/Fe] are milder than previous estimates because of the application of nonsolar abundance corrections to both Mg b and Fe for the first time. While [E/Fe] is usually greater than zero, it is not the "E" elements that are actually enhanced but rather the Fe-peak elements that are depressed; this serves not only to weaken Fe but also to strengthen Mg b, accounting for the overall generally mild enhancements. Based on index strengths from the Lick/IDS galaxy library (Trager et al.), C is not depressed with Fe but rather seems to be on a par with other elements such as Mg in the E group. Gradients in stellar populations within galaxies are found to be mild, with SSP-equivalent age increasing by 25%, metallicity decreasing by [Z/H] = 0.20 dex, and [E/Fe] remaining nearly constant out to an aperture of radius re/2 for nearly all systems. Our ages have an overall zero-point uncertainty of at least ~25% because of uncertainties in the stellar evolution prescription, the oxygen abundance, the effect of [E/Fe] ≠ 0 on the isochrones, and other unknowns. However, the relative age rankings of stellar populations should be largely unaffected by these errors. In particular, the large spread in ages appears to be real and cannot be explained by contamination of Hβ by blue stragglers or hot horizontal-branch stars, or by fill-in of Hβ by emission. Correlations between these derived SSP-equivalent parameters and other galaxy observables will be discussed in future papers.

Absorption-Line Probes of Gas and Dust in Galactic Superwinds

Abstract: We have obtained moderate resolution (R = few thousand) spectra of the Na I λλ5890, 5896 (Na D) absorption line in a sample of 32 far-IR-bright starburst galaxies. In 18 cases, the Na D line in the nucleus is produced primarily by interstellar gas, while cool stars contribute significantly in the others. In 12 of the 18 "interstellar-dominated" cases the Na D line is blueshifted by over 100 km s-1 relative to the galaxy systemic velocity (the "outflow sources"), while no case shows a net redshift of more than 100 km s-1. The absorption-line profiles in these outflow sources span the range from near the galaxy systemic velocity to a maximum blueshift of ~400-600 km s-1. The outflow sources are galaxies systematically viewed more nearly face-on than the others. We therefore argue that the absorbing material consists of ambient interstellar material that has been entrained and accelerated along the minor axis of the galaxy by a hot starburst-driven superwind. The Na D lines are optically thick, but indirect arguments imply total hydrogen column densities of NH ~ few × 1021 cm-2. This implies that the superwind is expelling matter at a rate comparable to the star formation rate. This outflowing material is evidently very dusty: we find a strong correlation between the depth of the Na D profile and the line-of-sight reddening. Typical implied values are E(B-V) = 0.3-1 over regions several-to-10 kpc in size. We briefly consider some of the potential implications of these observations. The estimated terminal velocities of superwinds inferred from the present data and extant X-ray data are typically 400-800 km-1, are independent of the galaxy rotation speed, and are comparable to (substantially exceed) the escape velocities for L* (dwarf) galaxies. The resulting selective loss of metals from shallower potential wells can establish the mass-metallicity relation in spheroids, produce the observed metallicity in the intracluster medium, and enrich a general IGM to of order 10-1 solar metallicity. If the outflowing dust grains can survive their journey into the IGM, their effect on observations of cosmologically distant objects would be significant.

Star Formation in a Crossing Time

Abstract: Observations suggest that star formation occurs in only one or two crossing times for a range of scales spanning a factor of ~1000. These observations include (1) measurements of embedded cluster ages in comparison with the cloud core dynamical times, (2) measurements of the age difference versus separation for clusters in the Large Magellanic Clouds in comparison with the crossing time versus size correlation for molecular clouds, (3) the hierarchical structure of embedded young clusters, and (4) the high fraction of dense clouds that contain star formation. Such a short overall timescale for star formation implies that sources of turbulent energy or internal feedback are not required to explain or extend cloud lifetimes and that star and protostar interactions cannot be important for the stellar initial mass function. Stars appear in a cloud as if they freeze out of the gas, preserving the turbulent-driven gas structure in their birth locations. The Galaxy-wide star formation rate avoids the Zuckerman-Evans catastrophe, which has long been a concern for molecular clouds that evolve this quickly, because the multifractal structure of interstellar gas ensures that only a small fraction of the mass is able to form stars. Star formation on large scales operates more slowly than on small scales, but in most cases the whole process is over in only a few dynamical times.

Chandra X-Ray Observations of the Hydra A Cluster: An Interaction between the Radio Source and the X-Ray-emitting Gas

Abstract: We present Chandra X-ray observations of the Hydra A cluster of galaxies, and we report the discovery of structure in the central 80 kpc of the cluster's X-ray-emitting gas. The most remarkable structures are depressions in the X-ray surface brightness, approximately 25-35 kpc in diameter, that are coincident with Hydra A's radio lobes. The depressions are nearly devoid of X-ray-emitting gas, and there is no evidence for shock-heated gas surrounding the radio lobes. We suggest that the gas within the surface brightness depressions was displaced as the radio lobes expanded subsonically, leaving cavities in the hot atmosphere. The gas temperature declines from 4 keV at 70 kpc to 3 keV in the inner 20 kpc of the brightest cluster galaxy (BCG), and the cooling time of the gas is approximately 600 Myr in the inner 10 kpc. These properties are consistent with the presence of an approximately 34 M middle dot in circle yr-1 cooling flow within a 70 kpc radius. Bright X-ray emission is present in the BCG surrounding a recently accreted disk of nebular emission and young stars. The star formation rate is commensurate with the cooling rate of the hot gas within the volume of the disk, although the sink for the material that may be cooling at larger radii remains elusive. A bright, unresolved X-ray source is present in the BCG's nucleus, coincident with the radio core. Its X-ray spectrum is consistent with a power law absorbed by a foreground NH approximately 4x1022 cm-2 column of hydrogen. This column is roughly consistent with the hydrogen column seen in absorption toward the less, similar24 pc diameter VLBA radio source. Apart from the point source, no evidence for excess X-ray absorption above the Galactic column is found.

The SCUBA Local Universe Galaxy Survey – I. First measurements of the submillimetre luminosity and dust mass functions

Abstract: This is the first of a series of papers presenting results from the SCUBA Local Universe Galaxy Survey (SLUGS), the first statistical survey of the submillimetre properties of the local Universe. As the initial part of this survey, we have used the SCUBA camera on the James Clerk Maxwell Telescope to observe 104 galaxies from the IRAS Bright Galaxy Sample. We present here the 850-μm flux measurements. The 60-, 100-, and 850-μm flux densities are well fitted by single-temperature dust spectral energy distributions, with the sample mean and standard deviation for the best-fitting temperature being Td=35.6±4.9 K and for the dust emissivity index β=1.3±0.2. The dust temperature was found to correlate with 60-μm luminosity. The low value of β may simply mean that these galaxies contain a significant amount of dust that is colder than these temperatures. We have estimated dust masses from the 850-μm fluxes and from the fitted temperature, although if a colder component at around 20 K is present (assuming a β of 2), then the estimated dust masses are a factor of 1.5–3 too low. We have made the first direct measurements of the submillimetre luminosity function (LF) and of the dust mass function. Unlike the IRAS 60-μm LF, these are well fitted by Schechter functions. The slope of the 850-μm LF at low luminosities is steeper than −2, implying that the LF must flatten at luminosities lower than we probe here. We show that extrapolating the 60-μm LF to 850 μm using a single temperature and β does not reproduce the measured submillimetre LF. A population of ‘cold’ galaxies (Td<25 K) emitting strongly at submillimetre wavelengths would have been excluded from the 60-μm-selected sample. If such galaxies do exist, then this estimate of the 850-μm flux is biased (it is underestimated). Whether such a population does exist is unknown at present. We correlate many of the global galaxy properties with the FIR/submillimetre properties. We find that there is a tendency for less luminous galaxies to contain hotter dust and to have a greater star formation efficiency (cf. Young). The average gas-to-dust ratio for the sample is 581±43 (using both the atomic and molecular hydrogen), which is significantly higher than the Galactic value of 160. We believe that this discrepancy is probably due to a ‘cold dust’ component at Td≤20 K in our galaxies. There is a surprisingly tight correlation between dust mass and the mass of molecular hydrogen, estimated from CO measurements, with an intrinsic scatter of ≃50 per cent.

The Formation and Fragmentation of Primordial Molecular Clouds

Abstract: Many questions in physical cosmology regarding the thermal history of the intergalactic medium, chemical enrichment, reionization, etc., are thought to be intimately related to the nature and evolution of pregalactic structure. In particular, the efficiency of primordial star formation and the primordial initial mass function are of special interest. We present results from high-resolution three-dimensional adaptive mesh refinement simulations that follow the collapse of primordial molecular clouds and their subsequent fragmentation within a cosmologically representative volume. Comoving scales from 128 kpc down to 1 pc are followed accurately. Dark matter dynamics, hydrodynamics, and all relevant chemical and radiative processes (cooling) are followed self-consistently for a cluster-normalized cold dark matter (CDM) structure formation model. Primordial molecular clouds with ~105 solar masses are assembled by mergers of multiple objects that have formed hydrogen molecules in the gas phase with a fractional abundance of 10-4. As the subclumps merge, cooling lowers the temperature to ~200 K in a "cold pocket" at the center of the halo. Within this cold pocket, a quasi-hydrostatically contracting core with mass ~200 M☉ and number densities 105 cm-3 are found. We find that less than 1% of the primordial gas in such small-scale structures cools and collapses to sufficiently high densities to be available for primordial star formation. Furthermore, it is worthwhile to note that this study achieved the highest dynamic range covered by structured adaptive mesh techniques in cosmological hydrodynamics to date.

Unveiling the circumstellar envelope and disk: A subarcsecond survey of circumstellar structures

Abstract: We present the results of a λ = 2.7 mm continuum interferometric survey of 24 young stellar objects in 11 fields. The target objects range from deeply embedded class 0 sources to optical T Tauri sources. This is the first subarcsecond survey of the λ = 2.7 mm dust continuum emission from young, embedded stellar systems. These multiarray observations, utilizing the high dynamic u-v range of the BIMA array, fully sample spatial scales ranging from 04 to 60'', thus allowing the first consistent comparison of dust emission structures in a variety of systems. The images show a diversity of structure and complexity. The optically visible T Tauri stars (DG Tauri, HL Tauri, GG Tauri, and GM Aurigae) have continuum emission dominated by compact (≤1'') circumstellar disks. In the cases of HL Tauri and DG Tauri, the disks are resolved. The more embedded near-infrared sources (SVS 13 and L1551 IRS 5) have continuum emission that is extended and compact. The embedded sources (L1448 IRS 3, NGC 1333 IRAS 2, NGC 1333 IRAS 4, VLA 1623, and IRAS 16293-2422) have continuum emission dominated by the extended envelope, typically ≥85% of the emission at λ = 2.7 mm. In many of the deeply embedded systems, it is difficult to uniquely isolate the disk emission component from the envelope extending inward to AU-sized scales. Simple estimates of the circumstellar mass in the optical/infrared and embedded systems are in the ranges 0.01-0.08 M☉ and 0.04-2.88 M☉, respectively. All of the target embedded objects are in multiple systems with separations on scales of ~30'' or less. Based on the system separation, we place the objects in three categories: separate envelope (separation ≥6500 AU), common envelope (separation 150-3000 AU), and common disk (separation ≤100 AU). These three groups can be linked with fragmentation events during the star formation process: separate envelopes from prompt initial fragmentation and the separate collapse of a loosely condensed cloud, common envelopes from fragmentation of a moderately centrally condensed spherical system, and common disk from fragmentation of a high angular momentum circumstellar disk.

The Ultraviolet Spectrum of MS 1512–cB58: An Insight into Lyman-Break Galaxies*

Abstract: We present an intermediate-resolution, high signal-to-noise ratio spectrum of the z = 2.7268 galaxy MS 1512-cB58 obtained with the Low Resolution Imaging Spectrograph (LRIS) on the Keck I telescope and covering the rest frame far-UV from 1150 to 1930 A. Gravitational lensing by a foreground cluster boosts the flux from MS 1512-cB58 by a factor of ~30 and provides the opportunity for a first quantitative study of the physical properties of star-forming galaxies at high redshift. The spectrum we have recorded is very rich in stellar and interstellar features; from our analysis of them, we deduce the following main results. The ultraviolet spectral properties of MS 1512-cB58 are remarkably similar to those of nearby star-forming galaxies and spectral synthesis models based on libraries of O and B stars can reproduce accurately the fine detail of the integrated stellar spectrum. The P Cygni profiles of C IV and N V are best matched by continuous star formation with a Salpeter initial mass function (IMF) extending beyond M = 50 M☉—we find no evidence for either a flatter IMF (at the high-mass end) or an IMF deficient in the most massive stars. There are clues in our data that the metallicity of both the stars and the gas is a few times below solar. Our best estimate, ZcB58 ≈ Z☉, is ≈3 times higher than the typical metallicity of damped Lyα systems at the same redshift, which is consistent with the proposal that the galaxies which dominate the H I absorption cross section are generally forming stars at a slower rate than L* Lyman-break galaxies like MS 1512-cB58. The relative velocities of the stellar lines, interstellar absorption, and H II emission indicate the existence of large-scale outflows in the interstellar medium of MS 1512-cB58, with a bulk outward motion of 200 km s-1 and a mass-loss rate of ≈60 M☉ yr-1, which is roughly comparable to the star formation rate. Such galactic winds seem to be a common feature of starburst galaxies at all redshifts and may well be the mechanism that self-regulates star formation, distributes metals over large volumes, and allows the escape of ionizing photons into the intergalactic medium. We suggest further observations of MS 1512-cB58 that would provide more precise measurements of element abundances and of detailed physical parameters and highlight the need to identify other examples of gravitationally lensed galaxies for a comprehensive study of star formation at early times.

Starburst-driven galactic winds — I. Energetics and intrinsic X-ray emission

Abstract: Starburst-driven galactic winds are responsible for the transport of mass, in particular metal-enriched gas, and energy out of galaxies and into the intergalactic medium. These outflows directly affect the chemical evolution of galaxies, and heat and enrich the intergalactic and intercluster medium. Currently, several basic problems preclude quantitative measurements of the impact of galactic winds: the unknown filling factors of, in particular, the soft X-ray-emitting gas prevent accurate measurements of densities, masses and energy content; multiphase temperature distributions of unknown complexity bias X-ray-determined abundances; unknown amounts of energy and mass may reside in hard to observe T∼105 K and T∼107.5 K phases; and the relative balance of thermal versus kinetic energy in galactic winds is not known. In an effort to address these problems, we perform an extensive hydrodynamical parameter study of starburst-driven galactic winds, motivated by the latest observation data on the best-studied starburst galaxy M82. We study how the wind dynamics, morphology and X-ray emission depend on the ISM distribution of the host galaxy, the starburst star formation history and strength, and the presence and distribution of mass-loading by dense clouds. We also investigate and discuss the influence of finite numerical resolution on the results of these simulations. We find that the soft X-ray emission from galactic winds comes from low filling factor (η≲2 per cent) gas, which contains only a small fraction (≲10 per cent) of the mass and energy of the wind, irrespective of whether the wind models are strongly mass-loaded or not. X-ray observations of galactic winds do not directly probe the gas that contains the majority of the energy, mass or metal-enriched gas in the outflow. X-ray emission comes from a complex phase-continuum of gas, covering a wide range of different temperatures and densities. No distinct phases, as are commonly assumed when fitting X-ray spectra, are seen in our models. Estimates of the properties of the hot gas in starburst galaxies based on fitting simple spectral models to existing X-ray spectra should be treated with extreme suspicion. The majority of the thermal and kinetic energy of these winds is in a volume-filling hot, T∼107 K, component which is extremely difficult to probe observationally because of its low density and hence low emissivity. Most of the total energy is in the kinetic energy of this hot gas, a factor that must be taken into account when attempting to constrain wind energetics observationally. We also find that galactic winds are efficient at transporting large amounts of energy out of the host galaxy, in contrast to their inefficiency at transporting mass out of star-forming galaxies.

Multiwavelength Observations of Dusty Star Formation at Low and High Redshift

Abstract: If high-redshift galaxies resemble rapidly star-forming galaxies in the local universe, most of the luminosity produced by their massive stars will have been absorbed by dust and reradiated as far-infrared photons that cannot be detected with existing facilities. This paper examines what can be learned about high-redshift star formation from the small fraction of high-redshift galaxies' luminosities that is emitted at accessible wavelengths. We first consider the most basic ingredient in the analysis of high-redshift surveys: the estimation of star formation rates for detected galaxies. Standard techniques require an estimate of the bolometric luminosity produced by their massive stars. We review and quantify empirical correlations between bolometric luminosities produced by star formation and the UV, mid-IR, sub-mm, and radio luminosities of galaxies in the local universe. These correlations suggest that observations of high-redshift galaxies at any of these wavelengths should constrain their star formation rates to within ~0.2-0.3 dex. We assemble the limited evidence that high-redshift galaxies obey these locally calibrated correlations. The second part of the paper assesses whether existing surveys have found the galaxies that host the majority of star formation at high redshift even though they directly detect only a small fraction of the luminosities of individual galaxies. We describe the characteristic luminosities and dust obscurations of galaxies at z ~ 0, z ~ 1, and z ~ 3. After discussing the relationship between the high-redshift populations selected in surveys at different wavelengths, we calculate the contribution to the 850 ?m background from each and argue that these known galaxy populations can together have produced the entire observed background. The available data show that a correlation between star formation rate and dust obscuration Lbol,dust/LUV exists at low and high redshift alike. The existence of this correlation plays a central role in the major conclusion of this paper: most star formation at high redshift occurred in galaxies with moderate dust obscurations 1 Lbol,dust/LUV 100 similar to those that host the majority of star formation in the local universe and to those that are detected in UV-selected surveys.

Efficiencies of Low-Mass Star and Star Cluster Formation

Abstract: Using a quantitative model for bipolar outflows driven by hydromagnetic protostellar winds, we calculate the efficiency of star formation assuming that available gas is either converted into stars or ejected in outflows. We estimate the efficiency of a single star formation event in a protostellar core, finding 25%-70% for cores with various possible degrees of flattening. The core mass function and the stellar initial mass function have similar slopes because the efficiency is not sensitive to its parameters. We then consider the disruption of gas from a dense molecular clump in which a cluster of young stars is being born. In both cases, we present analytical formulae for the efficiencies that compare favorably against observations and, for clusters, against numerical simulations. We predict efficiencies in the range of 30%-50% for the regions that form clusters of low-mass stars. In our model, star formation and gas dispersal happen concurrently. We neglect the destructive effects of massive stars: our results are therefore upper limits to the efficiency in regions more massive than about 3000 M☉ .

Gravitational collapse in turbulent molecular clouds. I. gasdynamical turbulence

Abstract: Observed molecular clouds often appear to have very low star formation efficiencies and lifetimes an order of magnitude longer than their free-fall times. Their support is attributed to the random supersonic motions observed in them. We study the support of molecular clouds against gravitational collapse by supersonic, gasdynamical turbulence using direct numerical simulation. Computations with two different algorithms are compared: a particle-based, Lagrangian method (smoothed particle hydrodynamics [SPH]) and a grid-based, Eulerian, second-order method (ZEUS). The effects of both algorithm and resolution can be studied with this method. We find that, under typical molecular cloud conditions, global collapse can indeed be prevented, but density enhancements caused by strong shocks nevertheless become gravitationally unstable and collapse into dense cores and, presumably, stars. The occurrence and efficiency of local collapse decreases as the driving wavelength decreases and the driving strength increases. It appears that local collapse can be prevented entirely only with unrealistically short wavelength driving, but observed core formation rates can be reproduced with more realistic driving. At high collapse rates, cores are formed on short timescales in coherent structures with high efficiency, while at low collapse rates they are scattered randomly throughout the region and exhibit considerable age spread. We suggest that this naturally explains the observed distinction between isolated and clustered star formation.

Dark Halo and Disk Galaxy Scaling Laws in Hierarchical Universes

Abstract: We use cosmological N-body/gasdynamical simulations that include star formation and feedback to examine the proposal that scaling laws between the total luminosity, rotation speed, and angular momentum of disk galaxies reflect analogous correlations between the structural parameters of their surrounding dark matter halos. The numerical experiments follow the formation of galaxy-sized halos in two cold dark matter (CDM)-dominated universes: the standard Ω = 1 CDM scenario and the currently popular ΛCDM model. We find that the slope and scatter of the I-band Tully-Fisher relation are well reproduced in the simulations, although not, as proposed in recent work, as a result of the cosmological equivalence between halo mass and circular velocity: large systematic variations in the fraction of baryons that collapse to form galaxies and in the ratio between halo and disk circular velocities are observed in our numerical experiments. The Tully-Fisher slope and scatter are recovered in this model as a direct result of the dynamical response of the halo to the assembly of the luminous component of the galaxy. We conclude that models that neglect the self-gravity of the disk and its influence on the detailed structure of the halo cannot be used to derive meaningful estimates of the scatter or slope of the Tully-Fisher relation. Our models fail, however, to match the zero point of the Tully-Fisher relation, as well as that of the relation linking disk rotation speed and angular momentum. These failures can be traced, respectively, to the excessive central concentration of dark halos formed in the CDM cosmogonies we explore and to the formation of galaxy disks as the final outcome of a sequence of merger events. Disappointingly, our feedback formulation, calibrated to reproduce the empirical correlations linking star formation rate and gas surface density established by Kennicutt, has little influence on these conclusions. Agreement between model and observations appears to demand substantial revision to the CDM scenario or to the manner in which baryons are thought to assemble and evolve into galaxies in hierarchical universes.

Deep galaxy counts, extragalactic background light and the stellar baryon budget

Abstract: We assess the constraints imposed by the observed extragalactic background light (EBL) on the cosmic history of star formation and the stellar-mass density today. The logarithmic slope of the galaxy number–magnitude relation from the Southern Hubble Deep Field imaging survey is flatter than 0.4 in all seven UBVIJHK optical bandpasses, i.e. the light from resolved galaxies has converged from the UV to the near-IR. We find a lower limit to the surface brightness of the optical extragalactic sky of about 15 nW m−2 sr−1, comparable to the intensity of the far-IR background from COBE data. Assuming a Salpeter initial mass function with a lower cut-off consistent with observations of M subdwarf disc stars, we set a lower limit of Ωg+sh2>0.0013 I50 to the visible (processed gas + stars) mass density required to generate an EBL at a level of 50 I50 nW m−2 sr−1; our ‘best-guess’ value is Ωg+sh2≈0.0031 I50. Motivated by the recent microlensing results of the MACHO collaboration, we consider the possibility that massive dark haloes around spiral galaxies are composed of faint white dwarfs, and show that only a small fraction (≲5 per cent) of the nucleosynthetic baryons can be locked in the remnants of intermediate-mass stars forming at zF≲5, as the bright early phases of such haloes would otherwise overproduce the observed EBL.

Multi-wavelength Observations of Dusty Star Formation at Low and High Redshift

Abstract: This paper examines what can be learned about high-redshift star formation from the small fraction of high-redshift galaxies' luminosities that is emitted at accessible wavelengths. We review and quantify empirical correlations between bolometric luminosities produced by star formation and the UV, mid-IR, sub-mm, and radio luminosities of galaxies in the local universe. These correlations suggest that observations of high-redshift galaxies at any of these wavelengths should constrain their star-formation rates to within 0.2--0.3 dex. We assemble the limited evidence that high-redshift galaxies obey these locally calibrated correlations. The characteristic luminosities and dust obscurations of galaxies at z ~ 0, z ~ 1, and z ~ 3 are reviewed. After discussing the relationship between the high-redshift populations selected in surveys at different wavelengths, we calculate the contribution to the 850um background from each. The available data show that a correlation between star-formation rate and dust obscuration L_dust/L_UV exists at low and high redshift. This correlation plays a central role in the major conclusion of this paper: most star formation at high redshift occurred in galaxies with 1 < L_dust/L_UV < 100 similar to those that host the majority of star formation in the local universe and to those that are detected in UV-selected surveys. (abridged)

On the Cosmic Origins of Carbon and Nitrogen

Abstract: We analyze the behavior of N/O and C/O abundance ratios as a function of metallicity as gauged by O/H in large, extant Galactic and extragalactic H II region abundance samples. We compile and compare published yields of C, N, and O for intermediate mass and massive stars and choose appropriate yield sets based on analytical chemical evolution models fitted to the abundance data. We then use these yields to compute numerical chemical evolution models that satisfactorily reproduce the observed abundance trends and thereby identify the most likely production sites for carbon and nitrogen. Our results suggest that carbon and nitrogen originate from separate production sites and are decoupled from one another. Massive stars (M > 8 M☉) dominate the production of carbon, while intermediate-mass stars between 4 and 8 M☉, with a characteristic lag time of roughly 250 Myr following their formation, dominate nitrogen production. Carbon production is positively sensitive to metallicity through mass-loss processes in massive stars and has a pseudo-secondary character. Nitrogen production in intermediate mass stars is primary at low metallicity, but when 12 + log(O/H) > 8.3, secondary nitrogen becomes prominent, and nitrogen increases at a faster rate than oxygen—indeed, the dependence is steeper than would be formally expected for a secondary element. The observed flat behavior of N/O versus O/H in metal-poor galaxies is explained by invoking low star formation rates that flatten the age-metallicity relation and allow N/O to rise to observed levels at low metallicities. The observed scatter and distribution of data points for N/O challenge the popular idea that observed intermittent polluting by oxygen is occurring from massive stars following star bursts. Rather, we find most points cluster at relatively low N/O values, indicating that scatter is caused by intermittent increases in nitrogen caused by local contamination by Wolf-Rayet stars or luminous blue variables. In addition, the effect of inflow of gas into galactic systems on secondary production of nitrogen from carbon may introduce some scatter into N/O ratios at high metallicities.

The Radiative Feedback of the First Cosmological Objects

Abstract: In hierarchical models of structure formation, an early cosmic UV background (UVB) is produced by the small K) halos that collapse before reionization. The UVB at energies below 13.6 eV sup- (T vir ( 104 presses the formation of stars or black holes inside small halos by photodissociating their only cooling agent, molecular We self-consistently compute the buildup of the early UVB in Press-Schechter H 2 . models, coupled with photodissociation both in the intergalactic medium (IGM) and inside virialized H 2 halos. We —nd that the intergalactic has a negligible eUect on the UVB, both because its initial H 2 optical depth is small and because it is photodissociated at an early stage. If the UV sources in ((0.1) the —rst collapsed halos are stars, then their UV —ux suppresses further star formation inside small halos. This results in a pause in the buildup of the UVB, and reionization is delayed until larger halos (T vir Z 104 K) collapse. If the small halos host miniquasars with hard spectra extending to D1 keV, then their X-rays balance the eUects of the UVB, the negative feedback does not occur, and reionization could be caused by the small halos. Subject headings: cosmology: theorydiUuse radiationearly universegalaxies: formation ¨ molecular processesradiative transfer

2MASS Observations of the Perseus, Orion A, Orion B, and Monoceros R2 Molecular Clouds

Abstract: We use the 2MASS Second Incremental Release Point Source Catalog to investigate the spatial distribution of young stars in the Perseus, Orion A, Orion B, and MonR2 molecular clouds. After subtracting a semiempirical model of the field star contamination from the observed star counts, stellar surface density maps are used to identify compact clusters and any stellar population found more uniformly distributed over the molecular cloud. Each cloud contains between two and seven clusters, with at least half of the cluster population found in a single, rich cluster. In addition, a distributed stellar population is inferred in the Orion A and MonR2 molecular clouds within the uncertainties of the field star subtraction with a surface density between 0.013 and 0.083 arcmin-2. Sensitivity calculations suggest, however, that the number of stars in the distributed population may be underestimated by a factor of 2 or more if stars have been forming with a Miller-Scalo IMF at a constant star formation rate for longer than 10 Myr. After considering the possible evolutionary status of the distributed population, the global star formation efficiency implied by the sum of the distributed and cluster populations ranges between 1% and 9% among the four clouds. The fraction of the total stellar population contained in clusters for the nominal extinction model ranges from ≈50% to 100% if the distributed population is relatively young (<10 Myr), to ≈25%–70% if it is relatively old (≈100 Myr). The relatively high fraction of stars contained in clusters regardless of the age of the distributed population, in conjunction with the young ages generally inferred for embedded clusters in nearby molecular clouds, indicates that a substantial fraction of the total stellar population in these regions has formed within the past few million years in dense clusters. This suggests that either the star formation rate in each these clouds has recently peaked if one assumes clouds have ages greater than 10 Myr or molecular clouds are younger than typically thought if one assumes that the star formation rate has been approximately constant in time.

Tidally Triggered Star Formation in Close Pairs of Galaxies

Abstract: We analyze optical spectra of a sample of 502 galaxies in close pairs and N-tuples, separated by ≤50 h-1 kpc. We extracted the sample objectively from the CfA2 redshift survey, without regard to the surroundings of the tight systems; we remeasure the spectra with longer exposures, to explore the spectral characteristics of the galaxies. We use the new spectra to probe the relationship between star formation and the dynamics of the systems of galaxies. The equivalent widths of Hα [EW(Hα)] and other emission lines anticorrelate strongly with pair spatial separation (ΔD) and velocity separation; the anticorrelations do not result from any large-scale environmental effects that we detect. We use the measured EW(Hα) and the starburst models of Leitherer et al. to estimate the time since the most recent burst of star formation began for galaxies in our sample. In the absence of a large contribution from an old stellar population to the continuum around Hα that correlates with the orbit parameters, the observed ΔD-EW(Hα) correlation signifies that starbursts with larger separations on the sky are, on average, older. We also find a population of galaxies with small to moderate amounts of Balmer absorption. These galaxies support our conclusion that the sample includes many aging bursts of star formation; they have a narrower distribution of velocity separations, consistent with a population of orbiting galaxies near apogalacticon. By matching the dynamical timescale to the burst timescale, we show that the data support a simple picture in which a close pass initiates a starburst; EW(Hα) decreases with time as the pair separation increases, accounting for the anticorrelation. Recent N-body/smoothed particle hydrodynamics simulations of interacting pairs suggest a physical basis for the correlation—for galaxies with shallow central potentials, they predict gas infall before the final merger. This picture leads to a method for measuring the duration and the initial mass function of interaction-induced starbursts: our data are compatible with the starburst models and orbit models in many respects, as long as the starburst lasts longer than ~108 yr and the delay between the close pass and the initiation of the starburst is less than a few times 107 yr. If there is no large contribution from an old stellar population to the continuum around Hα, the Miller-Scalo and cutoff (M ≤ 30 M☉) Salpeter initial mass functions (IMFs) fit the data much better than a standard Salpeter IMF.

Mapping the Evolution of High Redshift Dusty Galaxies with Submillimeter Observations of a Radio-Selected Sample

Abstract: Direct submillimeter imaging has recently revealed the 850 μm background to be mostly composed of a population of distant ultraluminous infrared galaxies, but identifying the optical/near-infrared (NIR) counterparts to these sources has proved difficult because of the poor submillimeter spatial resolution. However, the proportionality of both centimeter and submillimeter data to the star formation rate suggests that high-resolution radio continuum maps with subarcsecond positional accuracy can be exploited to locate submillimeter sources. In this paper we present results from a targeted SCUBA survey of microjansky radio sources in the flanking fields of the Hubble Deep Field. The sources were selected from the uniform (8 μJy at 1 σ) 1.4 GHz VLA image of Richards. Even with relatively shallow SCUBA observations (a 3 σ detection limit of 6 mJy at 850 μm), we were successful at making submillimeter detections of optical/NIR-faint (I 24 and K 21–22) radio sources, and our counts closely match the bright counts from submillimeter surveys. An important corollary is that a large fraction of the bright (>6 mJy) submillimeter sources in untargeted submillimeter surveys have extremely faint optical/NIR counterparts and hence are inaccessible to optical imaging and spectroscopy. However, redshift estimates can be made from the ratio of the submillimeter flux to the radio flux across the 100 GHz break in the spectral energy distribution. This procedure, which we refer to as millimetric redshift estimation, places the bright submillimeter population at z = 1–3, where it forms the high-redshift tail of the faint radio population. The star formation rate density (SFRD) due to ultraluminous infrared galaxies increases by more than 2 orders of magnitude from z ~ 0 to z ~ 1–3. The SFRD at high-redshift inferred from our >6 mJy submillimeter observations is comparable with that observed in the ultraviolet/optical.

A model of supernova feedback in galaxy formation

Abstract: ABSTRA C T A model of supernova feedback during disc galaxy formation is developed. The model incorporates infall of cooling gas from a halo, and outflow of hot gas from a multiphase interstellar medium (ISM). The star formation rate is determined by balancing the energy dissipated in collisions between cold gas clouds with that supplied by supernovae in a disc marginally unstable to axisymmetric instabilities. Hot gas is created by thermal evaporation of cold gas clouds in supernova remnants, and criteria are derived to estimate the characteristic temperature and density of the hot component and hence the net mass outflow rate. A number of refinements of the model are investigated, including a simple model of a galactic fountain, the response of the cold component to the pressure of the hot gas, pressure-induced star formation and chemical evolution. The main conclusion of this paper is that low rates of star formation can expel a large fraction of the gas from a dwarf galaxy. For example, a galaxy with circular speed ,50 km s 21 can expel ,60‐80 per cent of its gas over a time-scale of ,1 Gyr, with a star formation rate that never exceeds ,0.1 M( yr 21 . Effective feedback can therefore take place in a quiescent mode and does not require strong bursts of star formation. Even a large galaxy, such as the Milky Way, might have lost as much as 20 per cent of its mass in a supernova-driven wind. The models developed here suggest that dwarf galaxies at high redshifts will have low average star formation rates and may contain extended gaseous discs of largely unprocessed gas. Such extended gaseous discs might explain the numbers, metallicities and metallicity dispersions of damped Lyman a systems.

Accelerating Star Formation in Clusters and Associations

Abstract: We use our own, recently developed pre-main-sequence evolutionary tracks to investigate the star formation histories of relatively nearby associations and clusters. We first employ published luminosities and effective temperatures to place the known members of each region in the H-R diagram. We then construct age histograms detailing that region's history. The groups studied include Taurus-Auriga, Lupus, Chamaeleon, ρ Ophiuchi, Upper Scorpius, IC 348, and NGC 2264. This study is the first to analyze a large number of star-forming regions with the same set of theoretical tracks. Our investigation corroborates and extends our previous results on the Orion Nebula Cluster. In all cases, we find that star formation began at a relatively low level some 107 yr in the past and has more recently undergone a steep acceleration. This acceleration, which lasts several million years, is usually continuing through the present epoch. The one clear exception is the OB association Upper Scorpius, where the formation rate climbed upward, peaked, and has now died off. Significantly, this is also the only region of our list that has been largely stripped of molecular gas. The acceleration represents a true physical phenomenon that cannot be explained away by incompleteness of the samples; nor is the pattern of stellar births significantly affected by observational errors or the presence of unresolved binaries. We speculate that increasing star formation activity arises from contraction of the parent cloud. Despite the short timescale for acceleration, the cloud is likely to evolve quasi-statically. Star formation itself appears to be a critical phenomenon, occurring only in locations exceeding some threshold density. The cloud's contraction must reverse itself, and the remnant gas dissipate, in less than 107 yr, even for aggregates containing no massive stars. In this case, molecular outflows from the stars themselves presumably accomplish the task, but the actual dispersal mechanism is still unclear.

The initial mass function of low-mass stars and brown dwarfs in young clusters

Abstract: We have obtained images of the Trapezium Cluster (140'' × 140''; 0.3 pc × 0.3 pc) with the Hubble Space Telescope Near-Infrared Camera and Multi-Object Spectrometer (NICMOS). Combining these data with new ground-based K-band spectra (R = 800) and existing spectral types and photometry, we have constructed an H-R diagram and used it and other arguments to infer masses and ages. To allow comparison with the results of our previous studies of IC 348 and ρ Oph, we first use the models of D'Antona & Mazzitelli. With these models, the distributions of ages of comparable samples of stars in the Trapezium, ρ Oph, and IC 348 indicate median ages of ~0.4 Myr for the first two regions and ~1-2 Myr for the latter. The low-mass initial mass functions (IMFs) in these sites of clustered star formation are similar over a wide range of stellar densities (ρ Oph, n = 0.2-1 × 103 pc-3; IC 348, n = 1 × 103 pc-3; Trapezium, n = 1-5 × 104 pc-3) and other environmental conditions (e.g., presence or absence of OB stars). With current data, we cannot rule out modest variations in the substellar mass functions among these clusters. We then make the best estimate of the true form of the IMF in the Trapezium by using the evolutionary models of Baraffe et al. and an empirically adjusted temperature scale and compare this mass function to recent results for the Pleiades and the field. All of these data are consistent with an IMF that is flat or rises slowly from the substellar regime to about 0.6 M☉ and then rolls over into a power law that continues from about 1 M☉ to higher masses with a slope similar to or somewhat larger than the Salpeter value of 1.35. For the Trapezium, this behavior holds from our completeness limit of ~0.02 M☉ and probably, after a modest completeness correction, even from 0.01-0.02 M☉. These data include ~50 likely brown dwarfs. We test the predictions of theories of the IMF against (1) the shape of the IMF, which is not log-normal, in clusters and the field, (2) the similarity of the IMFs among young clusters, (3) the lowest mass observed for brown dwarfs, and (4) the suggested connection between the stellar IMF and the mass function of prestellar clumps. In particular, most models do not predict the formation of the moderately large numbers of isolated objects down to 0.01 M☉ that we find in the Trapezium.

The Chemical Evolution of the Globular Cluster ω Centauri (NGC 5139)

Abstract: We present abundances for 22 chemical elements in 10 red giant members of the massive Galactic globular cluster ω Centauri. The spectra are of relatively high spectral resolution and signal-to-noise. Using these abundances plus published literature values, abundance trends are defined as a function of the standard metallicity indicator iron. The lowest metallicity stars in ω Cen have [Fe/H] ~ -1.8, and the initial abundance distribution in the cluster is established at this metallicity. The stars in the cluster span a range of [Fe/H] ~ -1.8 to -0.8. At the lowest metallicity, the heavy-element abundance is found to be well characterized by a scaled solar system r-process distribution, as found in other stellar populations at this metallicity. As iron increases, the s-process heavy-element abundances increase dramatically. Comparisons of the s-process increases with recent stellar models finds that s-process nucleosynthesis in 1.5–3 M⊙ asymptotic giant branch stars (AGB) fits well the heavy-element abundance distributions. In these low-mass AGB stars, the dominant neutron source is 13C(α, n)16O. A comparison of the Rb/Zr abundance ratios in ω Cen finds that these ratios are consistent with the 13C source. The reason ω Cen displays such a large s-process component is possibly due to the fact that in such a relatively low-mass stellar system, AGB ejecta, because of their low velocity winds, are more efficiently retained in the cluster relative to the much faster moving Type II supernova ejecta. Significant s-process enrichment relative to Fe, from the lower mass AGB stars, would require that the cluster was active in star formation for quite a long interval of time, of the order of 2–3 Gyr. The AGB ejecta were mixed with the retained fraction of Type II supernova ejecta and with the residual gas of initial composition. The analysis of α-rich elements shows that no significant amounts of Type Ia supernova debris were retained by the cluster. In this context, interpretation of the low and constant observed [Cu/Fe] ~ -0.6 (derived here for the first time in this cluster) finds a plausible interpretation.

The Mass Assembly and Star Formation Characteristics of Field Galaxies of Known Morphology

Abstract: We discuss a new method for inferring the stellar mass of a distant galaxy of known redshift based on the combination of a near-infrared luminosity and multi-band optical photometry. The typical uncertainty for field galaxies with I<22 in the redshift range 0

A population of very young brown dwarfs and free‐floating planets in Orion

Abstract: We describe the results of a very deep imaging survey of the Trapezium cluster in the IJH bands, using the UKIRT high-resolution camera UFTI. Approximately 32 per cent of the 515 point sources detected are brown dwarf candidates, including several free-floating objects with masses below the deuterium-burning (planetary) threshold at 0.013 M⊙, which are detectable because of their extreme youth. We have confidence that almost all the sources detected are cluster members, since foreground contamination is minimal in the 33-arcmin2 area surveyed, and the dense backdrop of OMC-1 obscures all background stars at these wavelengths. Extinction is calculated from the (J−H) colours, permitting accurate luminosity estimates, and temperatures are derived from the dereddened (I−J) colours. There is some evidence for a cut-off in the luminosity function below the level corresponding to several Jupiter masses, which may represent the bottom end of the initial mass function. Since star formation is complete in the Trapezium, this limit could have wide significance, if confirmed. However, it could well be an effect of the dispersal of the molecular cloud by the central O-type stars, a process for which the time-scale will vary between star formation regions.

Modelling star formation and feedback in simulations of interacting galaxies

Abstract: ABSTRA C T We discuss a heuristic model to implement star formation and feedback in hydrodynamical simulations of galaxy formation and evolution. In this model, gas is allowed to cool radiatively and to form stars at a rate given by a simple Schmidt-type law. We assume that supernova feedback results in turbulent motions of gas below resolved scales, a process that can pressurize the diffuse gaseous medium effectively, even if it lacks substantial thermal support. Ignoring the complicated detailed physics of the feedback processes, we try to describe their net effect on the interstellar medium with a fiducial second reservoir of internal energy, which accounts for the kinetic energy content of the gas on unresolved scales. Applying the model to three-dimensional, fully self-consistent models of isolated disc galaxies, we show that the resulting feedback loop can be modelled with smoothed particle hydrodynamics such that converged results can be reached with moderate numerical resolution. With an appropriate choice of the free parameters, Kennicutt’s phenomenological star formation law can be reproduced over many orders of magnitude in gas surface density. We also apply the model to mergers of equal-mass disc galaxies, typically resulting in strong nuclear starbursts. Confirming previous findings, the presence of a bulge can delay the onset of the starburst from the first encounter of the galaxies until their final coalescence. The final density profiles of the merger remnants are consistent with de Vaucouleurs profiles, except for the innermost region, where the newly created stars give rise to a luminous core with stellar densities that may be in excess of those observed in the cores of most elliptical galaxies. By comparing the isophotal shapes of collisionless and dissipative merger simulations we show that dissipation leads to isophotes that are more discy than those of corresponding collisionless simulations.